The goal showcased the Uruguayan's flair for improvisation, as he hooked the ball into the net from a prone position after slipping as he shaped to shoot.
Top scorer Sturridge added a second three minutes later, turning Damien Delaney inside out before lashing home his fifth league goal of the season.
Captain Steven Gerrard made it 3-0 with a 38th-minute penalty, taking his tally of Premier League goals to 99, before substitute Dwight Gayle replied for the visitors with a late glancing header.
Victory took Brendan Rodgers's side a point clear of Arsenal, who can reclaim top spot if they avoid defeat at West Bromwich Albion on Sunday.
Liverpool manager Rodgers heralded strike duo Suarez and Sturridge, saying: ``They were exceptional today. Their combination play was outstanding and they are right up there with the best in this league.''
Earlier, Manchester City bounced back from defeats by Aston Villa and Bayern Munich to end Everton's unbeaten start to the season with a 3-1 win at the Etihad Stadium.
Everton took a 16th-minute lead through on-loan Chelsea striker Romelu Lukaku, but Alvaro Negredo equalised immediately from Yaya Toure's fine reverse pass.
City lost captain Vincent Kompany to injury, but Sergio Aguero put the hosts ahead just before the interval.
A foul by Seamus Coleman on Pablo Zabaleta gave Aguero a chance to extend City's lead from the penalty spot in the 69th minute and although Tim Howard turned his shot onto the post, the ball bounced against the American goalkeeper and into the net for an own goal.
"Equalising immediately was important, but more important was the character of the team, playing against Everton _ the only unbeaten team in the league,'' said City manager Manuel Pellegrini.
"After a defeat (by Bayern) on Wednesday, it was important for me to see how the players reacted.''
Loic Remy scored twice in the space of eight first-half minutes as Newcastle United claimed a first win in three games with a 2-1 victory at Cardiff City, who replied through Peter Odemwingie.
Fulham climbed out of the relegation zone after a neat 83rd-minute strike from Darren Bent secured a 1-0 win at home to Stoke City, while Aston Villa were held to a 0-0 draw at Hull City.
-AAP